Subgroup Growth in Some Profinite Chevalley Groups

2015/11/13 by Capdeboscq, Inna, Kirkina, Karina, Rumynin, Dmitriy
#17B45 #17B70 (Secondary) #20E07 (Primary) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1511.04333

Abstract

In this article we improve the known uniform bound for subgroup growth of Chevalley groups over G(\mathbbF_p[[t]]). We introduce a new parameter, the ridgeline number v(G), and give new bounds for the subgroup growth of G(\mathbbF_p[[t]]) expressed through v(G). We achieve this by deriving a new estimate for the codimension of [U,V] where U and V are vector subspaces in the Lie algebra of G.

Related

• Growth in Chevalley groups relatively to parabolic subgroups and some applications
• Commensurability growths of algebraic groups
• Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with Applications to Derangements
• Characteristic Subgroup Growth
• Subgroup growth of lattices in semisimple Lie groups